A sample of 40 has category counts (5,8,12,15) across four categories. A chi-square goodness-of-fit test checks all category probabilities equal to 1/4. Which null reference law and statistic value are correct?
Expected counts are 10 each. Pearson statistic=Σ(O−E)²/E=(25+4+4+25)/10=5.8. With four categories, one total-count constraint and no fitted parameters, the asymptotic null law is χ²_(4−1)=χ²₃. **A**. The chi-square reference is asymptotic, not the exact finite multinomial law.
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